262 
Mr Sears, On the Longitudinal Impact 
only d^th of an inch and, the radius of the suspension being 
60 inches, an increase in its length of only 1 in 18,000 would 
cause an error of 10°/ o in the height of fall, or of 5°/ 0 in the 
velocity. With 2 " withdrawal the end-effect is about secs., 
and this I found to vary roughly as the inverse fifth root of 
the velocity (the law given by Hertz for the impact of spheres), 
so that the above would correspond to an error of l°/ 0 in the end- 
effect, or to ^ secs, in the duration of the impact. This error 
would increase as the inverse square of the velocity, or withdrawal. 
secs, corresponds roughly with one small division (§ mm.) on 
the galvanometer scale, and was consequently quite measurable. 
The usual range of variation, in sets of similar experiments, was 
only about two of these divisions, and, provided the withdrawal 
was not less than 2", this was not exceeded. The times given in 
this paper are, for the most part, the mean values of five or six 
observations, and are consequently almost certainly correct to well 
within secs. The deduced values of the wave-velocities are 
10 ® 
probably correct to within ^°/ o . 
With a withdrawal of 2" (corresponding to a max. pressure 
of about 108 tons to the sq. in.) the steel rods (with the exception 
of one pair) did not overstrain. A static test of a short specimen 
of the rod gave about 21 tons per sq. in. as the elastic limit of the 
steel in compression, so that it appears that stresses, of the 
extremely short duration involved in these experiments, may 
greatly exceed the elastic limit without producing any permanent 
set*. With copper and aluminium, on the other hand, over- 
straining could not be prevented and the readings diminished 
gradually with successive impacts until a steady value was reached. 
It appears, however, that, with careful treatment, the final state of 
the ends of the rods, due to the overstraining, is independent of 
their length, so that the straight line law still holds, and gives the 
correct value of the wave-velocity. In these cases two figures are 
given, the first being the initial reading ; and the second, the 
mean of several readings taken after the steady state had been 
reached. It will be seen that two straight lines are thus obtained 
which are practically parallel (Fig. 7). The value of the wave- 
velocity is taken from the second of these, more reliance being 
placed on this as each reading is the mean of several observations. 
Moreover, the overstraining takes place more or less irregularly 
* This is in agreement with Prof. Hopkinson’s observations for momentary 
tensions. 
